This day and age, no.
However, due to their long history of success. They are a blue blood of college football.
I think my gripe is much like everyone else that hates ND. They have been catered to by the writers and the powers of CFB and they need to be on the same playing field as everyone else. Back in the 80's-90's when they signed the exclusive NBC TV contract, I understand why they didn't join a conference. Now with conference tv deals, and affiliations, it is not as lucrative to be an independent. CFB needs to tell them, no special considerations will be given, if you are ranked in the top 4 when time comes, you get in, but conference champions, and strength of schedule will play a part.